Acinetobacter baumannii is a dangerous bacterial pathogen possessing the ability to persist on various surfaces, especially in clinical settings, and to rapidly acquire the resistance to a broad spectrum of antibiotics. Thus, the epidemiological surveillance of A. baumannii within a particular hospital, region, and across the world is an important healthcare task that currently usually includes performing whole-genome sequencing (WGS) of representative isolates. During the past years, the dissemination of A. baumannii across the world was mainly driven by the strains belonging to two major groups called the global clones or international clones (ICs) of high risk (IC1 and IC2). However, currently nine ICs are already considered. Although some clones were previously thought to spread in particular regions of the world, in recent years this is usually not the case. In this study, we determined five ICs, as well as three isolates not belonging to the major ICs, in one multidisciplinary medical center within the period 2017–2019. We performed WGS using both short- and long-read sequencing technologies of nine representative clinical A. baumannii isolates, which allowed us to determine the antibiotic resistance and virulence genomic determinants, reveal the CRISPR/Cas systems, and obtain the plasmid structures. The phenotypic and genotypic antibiotic resistance profiles are compared, and the possible ways of isolate and resistance spreading are discussed. We believe that the data obtained will provide a better understanding of the spreading and resistance acquisition of the ICs of A. baumannii and further stress the necessity for continuous genomic epidemiology surveillance of this problem-causing bacterial species.